Alignment-insensitive self-converging in-line color display

ABSTRACT

A television display arrangement includes a kinescope comprising a viewing screen, an in-line electron beam gun assembly for producing a plurality of electron beams and an envelope defining a neck, at one end of which the electron gun assembly is mounted. A deflection yoke is associated with the kinescope for producing astigmatic deflection fields for substantially converging the beams at all points on the viewing screen. The astigmatic fields have balanced nonuniformity functions with low peak excursions for reducing the sensitivity of the beam convergence to the position of the yoke relative to the electron beams, by which relative movement between the yoke and the kinescope does not substantially affect the convergence.

This is a continuation of application Ser. No. 070,311, filed Aug. 27,1979, now abandoned.

BACKGROUND OF THE INVENTION

This invention relates to self-converging color picture tube orkinescope display systems that do not require precise transverse, ortilt, alignment between the deflection yoke and the electron beams ofthe kinescope.

Color television kinescopes or picture tubes create color images bycausing electrons to impinge upon phosphors having different-wavelengthemissions. Normally, phosphors having red, green and blue-light emissionare used, grouped into trios or triads of phosphor areas, with eachtriad containing one phosphor area of each of the three colors.

In the kinescope, the phosphors of each of the three colors are excitedby an electron beam which is intended to impinge upon phosphors emittingonly one color. Thus, each electron beam may be identified by the coloremitted by the phosphor which the beam is intended to excite. The areaimpinged on by each electron beam is relatively large compared with aphosphor triad, and at any position on the screen, each beam excites aparticular color phosphor in each of several triads. The three electronbeams are generated by three electron guns located in a neck portion ofthe kinescope opposite the viewing screen formed by the phosphors. Theelectron guns are oriented so that the undeflected beams leave the gunassembly in converging paths directed towards the viewing screen. Forthe viewing screen to display a faithful color reproduction of a sceneit is necessary that the beam position relative to the kinescope beadjusted for producing color purity and static beam convergence at thecenter of the screen. The purity adjustment involves causing each of thered, green and blue beams to excite only its respective phosphor. Thisis accomplished by the shadow mask. The shadow mask is a screen or grillhaving large numbers of perforations through which the electron beamsmay pass. Each perforation is in a fixed position relative to each triadof color phosphor areas. The electron beams pass through one or more ofthe perforations and fall upon the appropriate color phosphors basedupon their directions of incidence. Color purity depends upon a highorder of accuracy in the placement of the phosphor triads relative tothe perforations and the apparent source of the electron beams.

Static convergence involves causing the three beams to converge at onescanning spot at or near the center of the viewing screen. Convergenceat the center of the screen may be accomplished by the use of a staticconvergence assembly mounted relative to the neck of the kinescope andadjusted or magnetized to produce a static magnetic field which causesthe three beams to converge at the center of the viewing screen.

In order to form a two-dimensional image, the luminescent spot excitedon the viewing screen by the three converged electron beams must bescanned both horizontally and vertically over the viewing screen to forma luminescent raster area. This is accomplished by means of magneticfields produced by a deflection yoke mounted upon the neck of thekinescope. The deflection yoke deflects the electron beams withsubstantially independent horizontal and vertical deflection systems.Horizontal deflection of the electron beams is provided by coils of theyoke which produce a magnetic field having mainly vertically-directedfield lines. The magnetic field intensity is varied with time at arelatively high rate. Vertical deflection of the electron beams isaccomplished by coils producing mainly a horizontally-directed magneticfield which varies with time at a relatively low rate. A permeablemagnetic core is associated with the yoke coils. The conductors of thecoils may enclose the core to form a toroidal deflection winding, or theconductors may form saddle coils which do not enclose the core.

The kinescope viewing screen is relatively flat. The electrons of eachelectron beam will traverse a greater distance when deflected towardsthe edge of the viewing screen than when directed toward the center. Dueto the separation of the electron guns, this may result in a separationof the landing points of the three electron beams when near or deflectedtowards the edge of the screen. In addition, prior art almost-uniformmagnetic deflection fields caused the electron beams to be overconvergedwhen deflected away from the center of the screen. These effects combineto cause the light spots of the three beams at points on the viewingscreen away from the center to be separated. This is known asmisconvergence and results in color fringes about the edges of thedisplayed images. A certain amount of misconvergence is tolerable, butcomplete separation of the three illuminated spots is generally notacceptable. Misconvergence may be measured as a separation of theideally superimposed red, green and blue lines of a crosshatch patternof lines appearing on the screen when an appropriate test signal isapplied to the picture tube. Each of the three electron beams scans araster, which may be identified by its color. Thus, a green raster isordinarily scanned by the center electron beam, and the outside beamsscan red and blue rasters. The crosshatch pattern is formed in each ofthe red, green and blue rasters. The crosshatch pattern outlines theraster with vertical and horizontal lines, and also includes othervertically and horizontally-directed lines, some of which pass throughthe center of the raster.

Formerly, kinescopes had the electron guns in a triangular or deltaconfiguration. Convergence of the electron beams at points away from thecenter of the viewing screen was accomplished in delta-gun systems bydynamic convergence arrangements including additional convergence coilsmounted about the neck of the kinescope and driven at the deflectionrates by dynamic convergence circuits to excite pole pieces locatedwithin the neck of the kinescope to thereby impart corrective motion tothe beams, as described in U.S. Pat. No. 3,942,067 issued Mar. 2, 1976to Cawood.

As described in U.S. Pat. No. 3,789,258 issued Jan. 29, 1974 to Barbin,and in U.S. Pat. No. 3,800,176 issued Mar. 26, 1974 to Gross, et al.,current television display arrangements utilize an in-line electron gunassembly together with a deflection yoke arrangement includingdeflection windings for producing negative horizontal isotropicastigmatism and positive vertical isotropic astigmatism such that thebeams are substantially converged at all points on the raster. Thiseliminates the need for dynamic convergence apparatus in the colro TVdisplay system. However, the nonuniform magnetic fields providing theisotropic astigmatisms necessary for self-convergence make theconvergence dependent upon the position of the longitudinal axis of theyoke relative to the longitudinal axis of the undeflected beams. Thissensitivity and the normal manufacturing tolerances affecting beamposition in the tube, make it necessary to adjust the yoke transverselyto achieve the best compromise convergence. A description of themagnitude of the convergence change resulting from a change of theposition of the beams relative to the yoke axis appears in theaforementioned Barbin patent.

In order to provide clearance to allow the deflection yoke to be movedtransversely (or tilted, which is accomplished by a transversepositioning of the free end of the yoke) relative to the electron beamsin order to provide the best overall convergence over the surface of thescreen, the diameter of the inner contour of prior-art deflection yokesis made larger than that of the corresponding contour of the envelope ofthe kinescope by a small amount, such as between 2 and 6 mm.

It is desirable to reduce, insofar as possible, the amount of materialsused in the construction of deflection yokes. In order to accomplishthis, the deflection yoke should be designed to closely hug the neckportion of the kinescope. Due to manufacturing tolerances, the innerdesign contour of the deflection yoke must be larger than the nominalouter contour of the kinescope neck, such that the worst-case smallestinner diameter of the yoke will fit snugly over the worst-case maximumouter diameter of the neck. In such a design, the deflection yoke isconsidered as fitting substantially snugly over the neck of a kinescopeeven though a gap may occur between the average inner diameter of theyoke and the average diameter of the neck.

Such a snug-fitting yoke will have substantially all of the magneticflux generated by the coils within the neck of the kinescope. Adeflection yoke which does not fit snugly, on the other hand, hasmagnetic flux in the interstice between the yoke and the kinescope neck.Flux outside of the neck is not used for deflection and merely adds tothe total energy which must be stored in the yoke field in order toaccomplish a given amount of deflection. Since the stored energy must beperiodically added to and removed from the deflection yoke, increasedreactive scanning power is required and yoke losses correspondinglyincrease for yokes which do not fit snugly about the neck of thekinescope. A deflection yoke which fits snugly about the neck of thekinescope may, therefore, be driven by deflection circuits which supplyless reactive power, and will dissipate less yoke power. The resultingdisplay system may be expected to have higher deflection sensitivity andbe more reliable than displays with loose-fitting yokes. Theposition-sensitivity of the self-converging deflection windingsheretofore used required that the deflection yoke be adjusted by atransverse motion as described in order to accomplish the desiredconvergence and consequently it has not been possible to provide amass-produced self-converging yoke fitting snugly about the neck of akinescope.

Prior art convergence adjustments by positioning the self-convergingyoke relative to the beams have been made in various ways. As describedin the aforementioned Barbin patent, a kinescope may first be fittedwith the deflection yoke with which it is to be used. Static convergenceadjustments are then made, the yoke is then moved transversely invertical and/or horizontal directions to achieve best possibleconvergence and is then fixed in position by means such as glue or asuitable fastening arrangement. Such a yoke may at the time of itsmanufacture have been tested in conjunction with a standard kinescope toverify that its characteristics fall within a certain tolerance, i.e.,that it is not defective. In a color TV display system currentlyproduced by a major manufacturer, the Barbin technique is used in atwo-step fashion. In this system, the picture tube incorporates featuresby which it can be individually adjusted with a standard deflection yokeduring the last stage of manufacture, and yoke locating means are set inposition on the tube based upon this adjustment. This system also uses apre-aligned deflection yoke having mating locating means. In addition,an adjustable circuit associated with the yoke permits electricalcompensation for the effects of any remaining horizontal misalignment ofthe beams in the vertical deflection field. Since every tube and everydeflection unit is thus individually pre-aligned, any tube automaticallymatches with any deflection unit and presumably, the deflection unitonly has to be pushed onto the neck of the tube until it seats andrequires no further adjustment by the ultimate user.

It is desirable to eliminate this costly pre-alignment of eachindividual tube for the standard yoke. It is also desirable to provide aself-converging in-line gun television display system which achievessubstantial convergence of three beams over the whole raster without theneed for transverse or tilt adjustment of the yoke relative to theundeflected electron beams in the kinescope. A self-convergingdeflection yoke according to an embodiment of the invention not onlyrequires no transverse alignment or pre-alignment for best convergence,but is incapable of being aligned for self-convergence because motion ofthe yoke relative to the kinescope does not substantially affectconvergence. Heretofore, this result has been regarded asself-contradictory, for it was believed that the non-uniform deflectionfields necessary to achieve self-convergence by differential deflectionof the electron beams made the convergence dependent upon precisealignment of the yoke field with the longitudinal axis of theundeflected electron beams. For example, U.S. Pat. No. 4,060,836 issuedNov. 29, 1977 to Corbeij, et al., states that coincidence of the axes ofthe deflection field and the display tube is a condition to achievingconvergence without additional aids. As a result of the lack ofconvergence sensitivity, the self-converging yoke in one embodiment ofthe invention may fit snugly about the neck of the kinescope.

Incremental sensitivity of convergence to vertical and horizontal motionof the yoke about its centered position relative to the beams can bemeasured to yield a dimensionless ratio of convergence error of theouter beams divided by yoke motion. Ordinarily, convergence error ismeasured in millimeters, so the ratio represents mm error/mm yokemotion. Yoke motion in a single plane may result in a convergence errorat the ends of both directions of deflection. For example, horizontalmotion of the yoke from that positon which yields best convergence maycause a change or error in the width of the red raster relative to theblue as well as a relative change or error in height of these tworasters. In particular, horizontal displacement of the beams in the yokefield causes the raster scanned by the leading beam, i.e., the beamwhich is offset in the direction of displacement, to scan a raster whichis increased in width and height relative to that scanned by the laggingbeam. Similarly, a vertical motion of the yoke relative to the kinescopemay cause an apparent relative rotation or crossover of the centralhorizontal as well as vertical crosshatch lines displayed on the raster.In particular, a displacement of the beams upward in the yoke fieldcauses the central crosshatch lines scanned by the right-hand offsetbeam (as viewed from the screen or exit end of the yoke) to rotateclockwise, and those scanned by the left-hand beam to rotatecounterclockwise. Vertical movement downward reverses the directions ofrotation. Measurements have been made of the incremental sensitivity ofconvergence to motion of a number of recent display systems includingdeflection yokes. The results in mm/mm are summarized and tabulated asfollows:

    ______________________________________                                                 HORIZ. MOTION                                                                             VERT. MOTION                                                        Width    Height   Horiz.  Vert.                                    System     Error    Error    Crossover                                                                             Crossover                                ______________________________________                                        Hitachi    0.2      0.8      0.5     0.7                                      17V 90°                                                                semitoroidal                                                                  Philips 20AX                                                                             0.5      0.3      0.5     0.3                                      25V 110° saddle                                                        Philips 30AX                                                                             0.9      1.0      0.6     0.1                                      25V 110° saddle                                                         Some RCA systems not embodying the present                                   invention gave the following results:                                         XD4780 19V 90°                                                                    1.7      0.8      1.2     0.6                                      full toroidal                                                                 XD5000 13V 90°                                                                    0.6      0.7      0.5     0.5                                      semitoroidal                                                                  XP74-125Q  2.8      1.2      1.6     0.3                                      25V 110°                                                               full toroidal                                                                 ______________________________________                                    

The 20AX and XP74-125Q systems exhibit relatively low vertical crossovererrors because both the 20AX and XP74-125Q display systems are notcompletely self-converging but use dynamic convergence for top-bottomconvergence. The reduced height error in response to horizontal motionof the yoke and reduced vertical crossover error in response to verticalmotion result from the reduced vertical astigmatism made possible by theuse of dynamic convergence in the 20AX display system.

A mathematical description of the dimensioning of a self-converging yokeis provided by third-order aberration theory as follows. Third-orderaberration theory of magnetic deflection can be used to analyze theapproximate electron-optical performance of a yoke from its fielddistribution functions H₀ (z) and H₂ (z) which vary with the positionalong the longitudinal or z axis of the yoke as is described in twoarticles entitled "Errors of Magnetic Deflection" by J. Haantjes and G.J. Lubben (H&L) which respectively appeared in Philips Research Reports,Vol. 12, pp. 46-48, 1957 and in Vol. 14, pp. 65-97, 1959. The system ofnotation adopted herein follows that of H&L.

The deflection of the electron beams taking into account only H₀ (z),the main component of the deflecting field, is termed Gaussian and isdesignated X or Y. A more complete representation of the field includesH₂ (z), which represents the transverse nonuniformity of the yoke field.

While the description of a yoke field by the field distributionfunctions H₀ (z) and H₂ (z) is not rigorously applicable to totaldeflection angles greater than 75°, the trends indicated by this fielddescription are useful in outlining performance of mangetic deflectionsystems with wider total deflection angles, such as 90° and 110°.

The deflection fields are described by a power-series expansion aboutthe electron-optical axis of the yoke in such a manner that in thehorizontal plane (y=0) the horizontal deflection field is:

    H.sub.IIy =H.sub.II0 (z)+H.sub.II2 (z)x.sup.2 +. . .       (1)

where the yoke axis lies along the z-axis of the coordinate system, andthe vertical deflection field in the vertical plane (x=0) is:

    H.sub.Ix =H.sub.I0 (z)+H.sub.I2 (z)y.sup.2 +. . .          (2)

The subscript I refers to a magnetic field having its main component inthe x-direction i.e., the vertical deflection field, and subscript IIrefers to a field having its main component in the y-direction i.e., thehorizontal deflection field.

The general aberration expressions describe the differences Δx and Δy atthe viewing screen between the Gaussian deflection and the third-orderdeflection (i.e., with H₂ (z) taken into account). These expressions forΔx and Δy are simplified in the case of a kinescope with in-lineelectron beams by eliminating terms relating to entrance of the beamsinto the yoke field with slopes other than in the horizontal plane.

For in-line electron beams, the aberration expressions pertinent to theinvention are: ##EQU1## Here, X_(s) and Y_(s) are the Gaussiandeflections at the screen, x_(s) ' is the slope in the horizontal planeof the beam entering the yoke field and x_(s), y_(s) are the coordinatesor the landing point of the undeflected beam measured from the trace ofthe yoke axis on the screen. Equations (3) and (4) are partial, in thatonly terms relating to the invention, i.e., North-South (NS) pincushion,convergence (astigmatism and coma), and alignment sensitivity ofconvergence have been included. The aberration coefficients A₁ -A₁₈ andB₁ -B₁₈ can be expressed in integral form. The physical significance ofthe aberration coefficient becomes clear when the following simplifyingassumptions are made; (a) the main deflecting fields of the vertical andhorizontal coils are similar, i.e., H_(II0) (z)≈-CH_(I0) (z); and (b)their Gaussian deflections are substantially coincident so that X≈CY (ascale factor difference C≠1 does not affect the aberration coefficients,which include ratios of the field distribution functions). These areexcellent approximations for toroidal yokes, in which the vertical andhorizontal windings have the same axial length; and in the case ofsaddle or saddle-toroid windings, the shorter length of the verticalcoils is compensated by their larger inner diameter so theapproximations remain valid. The detailed winding distributions of thehorizontal and vertical coils are different, and as a result, theirnonuniformity functions are dissimilar; H_(II2) (z)≠-CH_(I2) (z).

The simplified aberration coefficients necessary for understanding theinvention are then:

    B.sub.2 +A.sub.3 =(λ/4D.sup.2)+2S.sub.II1 +S.sub.I1 ( 5) ##EQU2##

    A.sub.6 +B.sub.6 =(λ/3D)+2(S.sub.II2 +S.sub.I2)     (8)

    A.sub.7 =(3/2)-S.sub.II3                                   ( 9)

    B.sub.8 =-1/2+S.sub.I3                                     ( 10)

    A.sub.16 =-2S.sub.II4                                      ( 11)

    A.sub.18 =2S.sub.II4 -(1/D)                                (12)

    B.sub.17 =2S.sub.I4                                        ( 13)

    B.sub.18 =2S.sub.I4 -(1/D)                                 (14)

in which D is the distance from the principal plane of Gaussiandeflection to the screen, L is the effective length of the deflectionyoke, λ=L/D, and S₁, S₂, S₃ and S₄ are defined below.

The terms S_(IIi), S_(Ii) (i=1,2,3,4) are integral expressionscontaining the functions H_(II0), H_(II2) and H_(I0), H_(I2). Thus, forexample, North-South pincushion distortion is determined by thecoefficient B₂ +A₃ of equations (4) and (5), which includes both:

    S.sub.II1 =(1/X.sub.s.sup.3)∫H.sub.II2 X.sup.2 (z-z.sub.s)dz (15)

and

    S.sub.I1 =(1/Y.sub.s.sup.3)∫H.sub.I2 Y.sup.2 (z-z.sub.s)dz (16)

Here, X_(s) and Y_(s) are the Gaussian deflections on a viewing screenlocated at z_(s) with a distance D=(z_(s) -z_(c)) from the deflectioncenter z_(c) of the yoke, and z is distance measured along thelongitudinal axis of the yoke. H_(II2) and H_(I2) are the horizontal andvertical field nonuniformity functions respectively. The integration isformally performed from -∞ to +∞ but practically may be considered tobegin at a distance approximately one yoke diameter from the entrance ofthe yoke and to terminate at the screen.

Astigmatism in the horizontal direction is determined by the coefficientA₄, which in turn is partially determined by:

    S.sub.II2 =(1/X.sub.s.sup.2)∫H.sub.II2 X(z-z.sub.s).sup.2 dz (17)

Astigmatism in the vertical direction is determined by the coefficientB₅, which in turn is partially determined by:

    S.sub.I2 =(1/Y.sub.s.sup.2)∫H.sub.I2 Y(z-z.sub.s).sup.2 dz (18)

Coma is determined by:

    (horizontal)  S.sub.II3 =(1/X.sub.s)∫H.sub.II2 (z-z.sub.s).sup.3 dz (19)

    (vertical)  S.sub.I3 =(1/Y.sub.s)∫H.sub.I2 (z-z.sub.s).sup.3 dz (20)

These expressions describe the pincushion, astigmatism and comadistortions considered in the prior art for producing self-convergingyokes corrected for N-S pincushion and for coma.

Alignment sensitivity is determined by:

    (horizontal) S.sub.II4 =(1/X.sub.s)∫H.sub.II2 (z-z.sub.s).sup.2 dz (21)

    (vertical)  S.sub.I4 =(1/Y.sub.s)∫H.sub.I2 (z-z.sub.s).sup.2 dz (22)

While all portions of the yoke and its fields affect each of thedistortions, the effect of changes in particular regions of the fieldsmay affect particular distortions disproportionately.

This invention is based on the recognition that different portions ofthe H₂ -functions contribute differently to the sensitivity ofconvergence to misalignment of the yoke relative to the picture tube ofthe display system. Three yoke field regions are defined. The entranceregion extends from the exit of the electron gun to the vicinity of theentrance plane of the horizontal coils. The exit region extends from thevicinity of the exit plane of the core to the screen. The mid region isbounded by the entrance and exit planes.

The weighting functions appearing in the integrands of S_(IIi), S_(Ii)weight the H₂ -functions as shown in FIG. 1. Under the assumption ofsimilar main deflecting fields, only the horizontal weighting functionsneed be shown since the weighting functions for the vertical fieldcorrespond. In FIG. 1, the abscissa represents axial distance in thedisplay system measured from the deflection center z_(c) and theordinate represents the weighting function in arbitrary units. Thescreen is at a position z_(s) =10 inches (25.4 cm) from the deflectioncenter. The approximate position of the entrance and exit planes of adeflection yoke are indicated as EN and EX, respectively. The ordinatevalues are not the same for the different functions.

Equations (15) and (16) indicate that pincushion is determined mainly bythe behaviour of the H₂ -functions in the exit region and, to a smallerextent, in the mid region since the magnitudes of the negative weightingfunctions appearing in these equations, X² (z-z_(s)) and Y² (z-z_(s)),rise very steeply from their low values at the entrance, as illustratedin FIG. 1.

Equations (17) and (18) indicate that the astigmatism required forself-convergence is determined by portions of the H₂ -functions in themid and exit regions of the yoke since the positive weighting functionsX (z-z_(s))² and Y (z-z_(s))² rise rapidly from their values at theentrance.

Equations (19) and (20) indicate that coma is determined mainly by thebehaviour of the H₂ -functions in the entrance region and, to a smallerextent, in the mid region since the magnitude of the negative weightingfunction (z-z_(s))³ decreases rapidly from its maximum value at theentrance.

Equations (21) and (22) show that convergence sensitivity tomisalignment is determined by the behaviour of the H₂ -functions in theentrance and mid regions and, to a smaller extent, in the exit region,since the positive weighting function (z-z_(s))² decreases less rapidlyfrom its maximum value at the entrance.

Prior-art self-converging yokes for horizontal in-line gun displaysystems such as the RCA 19V90° toroidal yoke or the Hitachi 17V90°semitoroidal yoke, had field distribution functions as illustrated inFIGS. 2 and 3, respectively. As illustrated in FIGS. 2 and 3, the H_(I2)and H_(II2) functions are multiplied by a factor of 10 for clarity.

A qualitative discussion of prior art yokes can be based on theweighting functions illustrated in FIG. 1 in conjunction with FIGS. 2and 3. These yokes had horizontal field nonuniformity functions H_(II2)whose positive lobes (pincushion-shaped fields) exhibited excessivelylarge peaks in proximity to the entrance (EN) of the yoke. Such H_(II2)-functions produced the negative astigmatism required for convergence ofthe offset beams along the horizontal axis in an inefficient manner,since pincushion fields located near the entrance of the yoke, where thedeflection is still small, must have excessive nonuniformity to achieveself-convergence. This inefficient axial distribution of the H_(II2)-functions illustrated in FIGS. 2a and 3a led to sensitivity ofconvergence to misalignment of the beams in the horizontal fields andcontributed to horizontal coma. The aforementioned prior-art yokes hadvertical field nonuniformity functions H_(I2) with excessively largenegative values (barrel-shaped fields) near the entrance of the yoke,and in the case of toroidal vertical coils, as shown in FIGS. 2 and 3,all negative, unbalanced or single-lobe H_(I2) -functions. Such H_(I2)-functions produced the positive astigmatism required forself-convergence along the vertical axis inefficiently, since thecontribution of barrel fields at the entrance of the yoke to astigmatismis small, thus forcing the mid-yoke barrel fields to have excessivenonuniformity for achieving self-convergence. The consequences of thisinefficient axial distribution of the H₁₂ -functions illustrated inFIGS. 2b and 3b were substantial vertical coma, high sensitivity ofconvergence to misalignment of the beams in the vertical fields, and asignificant contribution to NS pincushion that was difficult to correctby the horizontal coils without causing "gullwing" orhigher-than-horizontal-frequency distortion of the raster top andbottom.

SUMMARY OF THE INVENTION

A television display arrangement includes a kinescope having a viewingscreen, an in-line electron gun assembly for producing a plurality ofelectron beams and an envelope defining a neck at one end of which anelectron gun assembly is mounted. A deflection yoke is associated withthe kinescope for producing astigmatic deflection fields forsubstantially converging the beams at all points on the viewing screen.The astigmatic fields each have minimized nonuniformity functions forreducing the sensitivity of the convergence to the position of the yokerelative to the electron beams, by which relative movement between theyoke and the kinescope does not affect the convergence.

DESCRIPTION OF THE DRAWING

FIG. 1 illustrates plots of weighting functions useful in explaining theregions significant to the various deflection errors;

FIGS. 2a, 2b, 3a and 3b are plots describing the deflection fielddistribution in prior art yokes;

FIGS. 4a and 4b illustrates plots describing the deflection fielddistribution in a yoke according to the invention;

FIG. 5 illustrates an elevation cross-section of a kinescope anddeflection yoke arrangement embodying the invention;

FIGS. 6a and 6b illustrate separate exit-end views of vertical andhorizontal windings, respectively, of a yoke embodying the invention,which views are not to scale in order to enhance clarity;

FIGS. 7a-7f illustrates in schematic form the winding distribution takenat three separate cross-sections of a yoke embodying the invention;

FIGS. 8a-8m is a preferred alternative representation of the windingdistribution of a yoke embodying the invention, together with a moredetailed representation of the turns distribution; and

FIGS. 9 and 10 are plots of the value of normalized Fourier fundamentaland third-harmonic coefficients as a function of longitudinal positionalong a yoke embodying the invention.

DESCRIPTION OF THE INVENTION

In accordance with the invention, yokes with non-geodesic windings,i.e., yokes having typical turns not lying on the shortest path betweentwo points on the inner surface of the coils, can be made to achieve theastigmatism required for self-or simplified convergence together withreduced coma and reduced top and bottom pincushion distortion and theconvergence of which is simultaneously insensitive to alignment errorsbetween the yoke fields and the electron beams of the kinescope.

These yokes eliminate coma and minimize sensitivity of convergence tomisalignment of the beams in the deflection fields by balancing theminimum mid and exit-region nonuniformities of the horizontal andvertical fields that are required for self-convergence and NSpincushion-correction with opposite nonuniformities at the entrance ofthe yoke. The horizontal H_(II2) -function has a smaller positiveportion in the mid region of the yoke, and the peak value of the H_(II2)-function occurs further toward the exit end than in the prior art. Thevertical H_(I2) -function includes a negative entrance lobe, a positivelobe immediately inside the entrance plane, and a mid-to-exit portion ofsmaller negative peak value than in the prior art, said negative peakoccurring closer to the exit than in the prior art. This axialdistribution of the H₂ -functions is more efficient, because itgenerates the magnitudes of negative horizontal and positive verticalastigmatism necessary for self-convergence with smaller peak value ofthe nonuniformity functions of horizontal pincushion and vertical barrelfields. This more efficient distribution of field nonuniformity offersadditional design freedom by comparison with prior art yokes, and thisdesign freedom is exploited to minimize the sensitivity of convergenceto misalignment of the beams in the yoke field, and to substantiallyeliminate horizontal and vertical coma and North-South pincushiondistortion of the raster.

The nonuniformity functions of the fields generated by yokes embodyingthe invention are subject to four requirements which can be describedmathematically. These requirements are as follows:

(1) According to the invention, North-South pincushion distortion isminimized by making:

    S.sub.II1 =-1/2(S.sub.I1)-(λ/8D.sup.2)              (23)

(2) The magnitudes of the negative horizontal and positive verticalastigmatism required for self-convergence are achieved by making:

    S.sub.II2 =(3/4D) to make A.sub.4 ≈0               (24)

    S.sub.I2 =(1/4D)-(1/2L) to make B.sub.5 ≈0         (25)

These conditions on A₄ =B₅ ≈0 are also used here as approximations forthe case of larger-screen displays, where A₄ is given a small positive,B₅ a small negative value in order to minimize A₆ +B₆ (underconvergencealong the horizontal, overconvergence along the vertical axis therebyachieving substantial convergence over the whole raster).

(3) Coma is eliminated by making:

    S.sub.II3 =(3/2) for A.sub.7 =0                            (26)

    S.sub.I3 =1/2for B.sub.8 =0                                (27)

(4) Elimination of convergence sensitivity to horizontal misalignmentrequires:

    S.sub.II4 =0 for A.sub.16 =0                               (28)

    S.sub.I4 =(1/2D) for B.sub.18 =0                           (29)

and elimination of convergence sensitivity to vertical misalignmentrequires:

    S.sub.II4 =(1/2D) for A.sub.18 =0 TM (30)

    S.sub.I4 =0 for B.sub.17 =0                                (31)

Since S_(I4) and S_(II4) cannot simultaneously equal both (1/2D) and 0,convergence sensitivity to both horizontal and vertical misalignment isminimized by making:

    S.sub.II4 =S.sub.I4 =(1/4D)                                (32)

The seven equations (23), (24), (25), (26), (27), and (32) are satisfiedby the "minimum-H₂ " fields generated by the new jokes. Assuming givenH_(IIo) =-CH_(Io) functions, these seven equations constitute a set oflinear integral equations whose solutions are the minimum -H₂ functionsproduced by yokes according to the invention.

A plot of the H₀ and H₂ functions of a deflection yoke according to anembodiment of the invention is illustrated in FIG. 4. In yokes embodyingthe invention, the vertical coils contribute a smaller amount of NSpincushion than do prior-art yokes, since their barrel fields in the midregion of the yoke have smaller nonuniformity, as can be seen from FIG.4a. This permits the horizontal coils with mid-yoke pincushion fields ofsmaller nonuniformity but extending over a larger region towards thescreen as shown in FIG. 4b to correct NS pincushion. This smallernonuniformity of both horizontal and vertical fields in the mid-to-exitregions permits achievement of self-convergence that is substantiallyinsensitive to the position of the beams relative to the fields.

FIG. 5 illustrates generally a kinescope 10 and a deflection yoke 16.Kinescope 10 includes an envelope having a neck portion 12 merging intoa flaring bulb portion 14. An electron gun assembly 13 represented as ablock 13 mounted in neck 12 produces horizontal in-line electron beamsin kinescope 10. Deflection yoke 16 is of the hybrid or saddle-toroidtype and includes horizontal windings 20, the electron-beam exit-endturns of which are illustrated as 22. The beam-entrance end turns areillustrated as 24. Vertical deflection windings 28 are toroidally woundabout a magnetic core 26. An insulator 18 interposed between horizontalwindings 20 and toroidally wound vertical windings 28 supports thewindings in position with respect to each other, and also provides means(not shown) by which the yoke assembly may be affixed to kinescope 10.In accordance with the invention, windings 20 and 28 are configured toprovide substantial insensitivity of convergence in response to verticalor horizontal transverse motion or tilting motion of yoke 16 relative tokinescope 10. Consequently, the gap illustrated as 32 between yoke 16and kinescope 10 does not have to be any larger than mechanical assemblytolerances require. As a result, no substantial vertical or horizontaltransverse motion of yoke 16 relative to kinescope 10 is possible.Similarly, no substantial tilting motion is possible. With such anarrangement, the yoke closely hugs the neck of the tube and lessmaterials may be required in its construction compared with thearrangement in which gap 32 is large. In an arrangement as in FIG. 5,more of the magnetic flux generated by the yoke is used for deflectionthan in the prior art. To achieve a given flux density within the neckof the kinescope for deflecting the electron beams, a smaller current isrequired than in the prior art and therefore the deflection sensitivityis increased and the circulation of energy between the yoke and thedrive circuits is reduced, and the total power dissipated in deflectionmay be minimized.

As is known, only those conductors of the vertical and horizontalwindings lying along the inner periphery of the magnetic core of adeflection yoke significantly affect the deflection. Consequently, thewinding distribution providing the benefits of the invention may beachieved with either toroidal or saddle windings.

FIG. 6a illustrates a horizontal deflection winding distribution of ayoke embodying the invention, and FIG. 6b illustrates a vertical windingdistribution thereof, as viewed from the large or beam-exit end of thedeflection yoke. From these views, it is difficult to discern thedistribution near the beam-entrance end, even though the entrance ringhas been made large to enhance clarity.

FIGS. 7a-7c illustrate two quadrants of the turns distribution at theentrance, mid and exit ends or regions, respectively, of the horizontalwindings of the yoke illustrated in FIG. 6. FIGS. 7d-7f illustrate twoquadrants of the turns distribution of the vertical deflection windingsat the entrance, mid and exit regions of the yoke of FIG. 6.

In FIG. 7a, the region marked 300 and 302 represents the region in whichturns of winding near the entrance end of the yoke occur. The linesmarked 304 and 306, respectively, represent the centroids of the actualwinding distribution rather than the centroid of areas 300 and 302. Asillustrated in FIG. 7a, winding distribution 302 subtends a centralangle of 70°, and the centroids 304,306 of the winding distributionitself occur at an angle of 35° from the horizontal, thereby indicatingthat the actual winding distributions are symmetrically disposed aboutthe centroids. Similarly, in FIG. 7b representing a cross-section nearthe mid region of the yoke, regions 310 represents the region in whichhorizontal windings occur. Each region 310 subtends a central angle of53° and starts at the horizontal plane. Line 312, representing the angleof the centroid of a winding distribution occurring within a region 310,is elevated 27° from the horizontal plane, thereby showing that thewinding distribution in region 310 is almost symmetrical. However, noindication is provided in such a representation to indicate whether thedistribution is concentrated at the ends of region 310, distributedevenly throughout, or is some other distribution. Similarly, FIG. 7cillustrates a winding distribution near the exit region of the yokeoccupying a region 324 which subtends a central angle of 24°, thecentroid of which winding distribution is 12.5° above the horizontal.Obviously, the winding distribution contained in region 324 is notsymmetrical, yet no indication of the actual distribution is given. FIG.7d illustrates regions 334 in which the vertical winding distribution islocated at a cross-section near the entrance end of the yoke. Regions334 each subtend a central angle of 58°. The centroid of each windingdistribution is located 24° from the vertical axis, which is not in thecenter of region 334. Similarly, FIG. 7e illustrates regions 344 inwhich the vertical winding distribution is located. Each region 344begins 6.6° from the vertical axis and subtends an angle of 68°. Thecentroid of the winding distribution in each region 344 is located on aline 342 lying 36.5° from the vertical axis and which is not near thecenter of region 344. FIG. 7f illustrates a corresponding distribution354 at the exit end of the yoke, the centroid 352 of which is near thecenter of the region 354 in which the winding distribution occurs. FromFIG. 7, it will be clear that a more detailed description of the windingdistribution is necessary to adequately describe their details.

FIG. 8 includes two alternate representations of a winding distributionaccording to the invention. FIGS. 8a-8f describe the horizontal windingdistribution, and FIGS. 8g-8m illustrate the vertical windingdistribution of a yoke according to the invention. FIGS. 8a, 8c, 8e, 8g,8i and 8k illustrate the actual conductor distribution, and FIGS. 8b,8d, 8f, 8n, 8j and 8m represent turns density distribution w_(H) andw_(V) derived from the conductor distribution. The horizontal axes ofthe graphs in FIG. 8 represent one quadrant around the periphery of theyoke. The quadrant is divided into 41 equal portions each of which isnumbered. These portions may represent actual channels into which theconductors or wires may be placed, or the portions may representindexing points at which a winding machine places wires. The zero markat the left of the horizontal axis represents the end of one quadrantand the beginning of the one shown, and the 41st mark at the rightrepresents the end of the quadrant shown and the beginning of another.The angle in degrees of the portions is also indicated. Conductors lyingon the zero axis are shown partially in solid and partially dotted, soas to indicate that portion of the conductor contributing to the fielddistribution in the quadrant in question. As illustrated, the conductorsare separated vertically as well as horizontally but in practice theymay be close-packed as required by practical winding considerations.

In FIG. 8, the wires illustrated are cross-sections of the wires of asingle wire wound to form either toroidal or saddle type windings.Consequently, the same current flows through all the wires. FIGS. 8a and8b illustrate the winding distribution near the exit end of the yoke.For this purpose, the exit end is at or near the end of the magneticcore. Wires 402 and 404 are located above the horizontal axis zero pointwhich divides one quadrant from another in FIG. 8a. For purposes ofanalysis, each contributes one-half a unit of current and thereforeone-half a turn to the quadrant shown, for a total of 1 turn. The firstdivision or portion of the quadrant of FIG. 8a also includes a thirdwire 406, which lies entirely within the first division and thereforecontributes a full turn. Contributions of turns are also provided bywires 407 and 408, which are illustrated as straddling the dividing linebetween the first and second portions of the quadrant. Consequently,wires 407 and 408 each contribute one-half turn, for a total of 1 turncontribution to the first division of the quadrant. Thus, the total turncontribution in the first division of quadrant of FIG. 8a is one-halfunit each from wires 402, 404 407 and 408, and a 1-unit contributionfrom wire 406. Total turn contribution from those wires associated withthe first division of quadrant thus totals 3 turns. FIG. 8b illustratesthe total turn contribution in the first division of the quadrant asbeing 3.

The second division of the quadrant in FIG. 8a includes the contributionof one-half turn each from wires 407 and 408, and one-half turn eachfrom wires 411 and 412, which straddle the division between the secondand third divisions of the quadrant. The second quadrant also receives afull turn contribution from windings 409 and 410, for a totalcontribution of 4 turns, as illustrated in FIG. 8b. The third divisionof FIG. 8a also has a 4-turn contribution, and the fourth divisionthrough the eleventh division each have a 3-turn contribution. Thetwelfth division includes one-half unit contribution from each ofwindings 414 and 416, for a total contribution of 1 turn as illustratedin FIG. 8b. The remaining portions of the quadrant contain no conductorsand the turn distribution is therefore zero. Thus, it can be seen thatthe turns distribution near the exit region of the actual yoke, asillustrated in FIG. 8a, may be represented by a discontinuous turn orwinding density distribution function W_(h) 420 as illustrated in FIG.8b.

FIG. 8c illustrates the actual turns distribution in one quadrant of ayoke embodying the invention in the mid region intermediate the entranceand exit ends of the yoke. Distribution 440 in FIG. 8d is acorresponding winding density distribution (W_(h)) representing the netcontribution of the windings shown in FIG. 8c. Similarly, the turnsdistribution illustrated in FIG. 8e represents the horizontal windingdistribution near the entrance region of the same yoke embodying theinvention as illustrated in FIGS. 8a and 8c. Distribution 460 of FIG. 8frepresents the winding density distribution (W_(h)) of FIG. 8e.

The vertical winding distribution (W_(v)) of a yoke embodying theinvention is shown in FIGS. 8g-8m. FIGS. 8g, 8i and 8k represent theactual winding distribution at the exit, mid and entrance ends of theyoke, respectively, and FIGS. 8h, 8j and 8m represent the correspondingwinding density distributions (W_(v)) 470, 480 and 490. Comparison ofFIGS. 8a-8f with FIGS. 7a-7c and FIGS. 8g-8m with FIGS. 7d-7f revealsthat the FIG. 7 representation of the winding distribution isoversimplified for a winding distribution such as those shown, in thatit omits important structural detail.

A mathematical characterization of the coils of a yoke is afforded by aFourier expansion of the winding distribution as known and as describedfor example in U.S. Pat. No. 4,117,434 issued Sept. 26, 1978 to Logan.That is, at a particular cross-section of the yoke, the discrete windingdistribution of the horizontal and vertical coils of the yokes embodyingthe invention can be described by Fourier series expansions of theirrespective winding densities: ##EQU3## where C_(n), S_(n) are theodd-order Fourier coefficients of the horizontal and vertical windingdensity distributions respectively, and w(φ) is the winding densitydistribution which means that w(φ) dφ is the number of turns in theinterval from φ to φ+dφ. The total number of turns N per quadrant (whichis, of course, the same in all cross-sections) is given by ##EQU4## Notethat the centroid of the winding density distribution is defined by

    φ.sub.H =∫φw.sub.H dφ/∫w.sub.H dφ

and the angle θ subtended between the centroids of the two halves of thecoil is θ=π-2φ_(H).

The coils of the XP75-125-CE 90° yoke, the winding distribution of whichis illustrated in FIGS. 4-6, and the coils of similar 90° yokesembodying the invention may be described by the fundamental and thirdharmonics of their winding densities in three cross-sections (entrance,mid, exit portions). To render this characterization independent of thecoil's impedance, the fundamental component is expressed as a fractionof the total number of turns in a quadrant and the third harmonic as afraction of the fundamental.

The coefficients listed below represent the normalized coefficients ofthe fundamental and third harmonics of the winding distribution at theentrance, mid and exit regions of a 90° toroidal yoke (XP75-125-CE)embodying the invention. The horizontal winding distribution isapproximated by the fundamental (^(C) 1/N_(H)) and third-harmonic (^(C)3/C₁) components, and the vertical winding distribution is approximatedby the fundamental (^(S) 1/N_(V)) and third-harmonic (^(S) 3/S₁)component.

    ______________________________________                                        XP75-125-CE                                                                          HORIZONTAL    VERTICAL                                                         ##STR1##                                                                           ##STR2##                                                                                   ##STR3##                                                                             ##STR4##                                     ______________________________________                                        entrance 0.99   -0.14        1.10 -0.26                                       mid      1.11   0.23         0.95 0.14                                        exit     1.24   0.80         0.67 1.43                                        ______________________________________                                    

These Fourier coefficients are plotted in FIG. 9 at three axialpositions (entrance, mid and exit regions) along the yoke.

Similarly, for a toroidal 110° yoke (XP75-128-ECQ) embodying theinvention, the coils are characterized by the coefficients:

    ______________________________________                                        XP75-128-ECQ                                                                         HORIZONTAL    VERTICAL                                                         ##STR5##                                                                           ##STR6##                                                                                   ##STR7##                                                                             ##STR8##                                     ______________________________________                                        entrance 0.94   -0.34        1.04 -0.17                                       mid      1.14   0.33         0.99 0                                           exit     1.25   0.87         0.69 1.42                                        ______________________________________                                    

which are plotted in FIG. 10.

Yokes according to the invention have horizontal coils whose windingdistributions are characterized by a fundamental Fourier component C₁/N_(H) of their winding density normalized to the total number of turnsper quadrant that increases from entrance to exit of the yoke, and by athird-harmonic Fourier component C₃ /C₁ normalized to the fundamentalthat has a negative value at the entrance of the yoke, turns positivebefore or at the mid region, and has its largest positive value near theexit of the yoke; and vertical coils whose winding distributions arecharacterized by a normalized fundamental Fourier component S₁ /N_(H)that decreases from entrance to exit of the yoke, and by a normalizedthird harmonic component S₃ /S₁ that has a negative value at theentrance of the yoke, turns positive before or at the mid region, andhas its largest positive value near the exit of the yoke.

The measured sensitivity of convergence of these yokes (mm/mm) is asfollows:

    ______________________________________                                                HORIZ. MOTION                                                                             VERT. MOTION                                                      Width  Height   Horiz.     Vert.                                              Error  Error    Crossover  Crossover                                  ______________________________________                                        XP75-125-CE                                                                             0        0.1      0.1      0                                        (19V 90°)                                                              XP75-128-ECQ                                                                            0.1      0.1      0.3      0.3                                      (25V 110°)                                                             ______________________________________                                    

which is substantially insensitive. For practical purposes, a horizontaldeflection winding may be said to have convergence insensitive to motionif transverse horizontal motion of the yoke or a corresponding tilt ofthe yoke relative to the electron beams in the kinescope causes verticalcrosshatch lines scanned by the two offset beams at each side of theraster of move horizontally relative to each other (size change) lessthan 0.4 mm per mm of motion, and vertical motion of the yoke relativeto the beams causes the ends of horizontal lines scanned by the offsetbeams through the center of the raster to move vertically relative toeach other less than 0.4 mm/mm. Similarly, a vertical deflection windingmay be said to be insensitive if horizontal motion of the yoke relativeto the beam causes horizontal crosshatch lines scanned by the two offsetbeams at the top and at the bottom of the raster to move verticallyrelative to each other less than 0.4 mm per mm of motion, and verticalmotion of the yoke causes the ends of vertical lines scanned by theoffset beams through the center of the raster to move horizontallyrelative to each other less than 0.4 mm/mm.

Saddle-type yokes may also be characterized by Fourier coefficients. Thequasi-continuous winding distributions of saddle coils in one quadrantof a yoke may be described by Fourier series expansion of their radialthickness in a constant-z plane representing one cross-section of thewinding.

T(φ)=ΣC_(n) cos n φ, where T(φ) is the thickness varying with the angleφ at any cross-section, and C_(n) is the Fourier coefficient of order n.The area A of any cross-section perpendicular to the inner contour R(z)of the saddle coil is constant, because the total number of wires is thesame at all cross-sections, and is given, to within (T)² <R, by ##EQU5##where R is the inner radius of the horizontal saddle coil at thecross-section in question, R'=dR/dz, and z is axial distance.

The horizontal saddle coils are characterized by the fundamental andthird harmonic Fourier coefficients of their radial thickness in threedefining cross-sections. Again, to normalize for impedance, thefundamental component of the cross-sectional area is expressed as afraction of the total cross-section, corresponding to normalization tothe number or quantity of windings, and the third harmonic coefficientis expressed as a fraction of the fundamental.

Other embodiments of the invention will be apparent to those skilled inthe art. In particular, described insensitive vertical windings may beused individually together with sensitive horizontal windings, and theinsensitive windings may be used in a yoke which is not snug-fitting.

What is claimed is:
 1. A color television display apparatus,comprising:a kinescope including an electron gun assembly for producingthree in-line electron beams; and a deflection yoke mounted upon saidkinescope, said yoke including entrance and exit ends and also includinghorizontal deflection conductors in a distribution about said kinescope,said distribution of horizontal deflection conductors being described ina quadrant by horizontal fundamental Fourier coefficients normalized tothe quantity of said horizontal deflection conductors in said quadrant,which normalized horizontal fundamental Fourier coefficients increase invalue from said entrance end to reach a maximum value near said exit endof said yoke, said distribution of said horizontal conductors also beingdescribed in said quadrant by horizontal third-harmonic Fouriercoefficients normalized to said horizontal fundamental coefficients ateach longitudinal position at which said horizontal third-harmoniccoefficients are established, said horizontal third-harmoniccoefficients having a negative value near the entrance-end of said yoke,and having a value which becomes increasingly positive at positionstowards the mid region of said yoke so as to take on a positive valuenear said mid region, and having a maximum positive value near said exitregion; said deflection yoke also including vertical deflectionconductors in a distribution about said kinescope, said verticaldistribution being described in a quadrant by vertical fundamentalFourier coefficients normalized to the quantity of said verticalconductors in said quadrant, which normalized vertical fundamentalFourier coefficients decrease in value from said entrance to said exitregions to reach a minimum value near said exit end of said yoke, saiddistribution of said vertical conductors also being described in saidquadrant by vertical third-harmonic Fourier coefficients normalized tothe value taken by said vertical fundamental Fourier coefficient at eachlongitudinal position at which said vertical third-harmonic Fouriercoefficients are established, said vertical third-harmonic Fouriercoefficients having values which are negative near said entrance-regionof said yoke, and which values take on increasingly more positive valuesat positions toward said mid region of said yoke, and having a maximumpositive value near said exit region, whereby the convergence of saidcolor display apparatus is rendered substantially insensitive to thetransverse position of said yoke relative to said kinescope.
 2. A colortelevision display apparatus, comprising:a kinescope including anelectron gun assembly for producing three in-line electron beams; and aself-converging and motion insensitive deflection yoke mounted on saidkinescope for passage therethrough by said electron beams, the passageof the electrons of said electron beams defining beam entrance and beamexit ends of said yoke which in turn are on either side of a mid-regionof said yoke, said yoke comprising horizontal and vertical deflectionwindings formed from turns of conductors, said turns of conductors beingwound to form distributions of conductors which vary from said entranceto said exit ends of said yoke, said distributions at any particularcross-section of said yoke taken perpendicular to the direction of saidbeams having axes of symmetry whereby the entire distribution at saidparticular cross-section can be substantially defined by describing theconductor distribution within one quadrant of said cross-section, saidconductor distributions being definable within any said quadrant interms of the sum of normalized fundamental and normalized third-harmonicFourier coefficients, said fundamental Fourier coefficients beingnormalized by dividing by the total number of windings for making theFourier representation independent of the total number of windings andtherefore independent of the impedance of the windings, said fundamentalFourier coefficients being representative of a conductor distributionwhich is a maximum at one end of a quadrant and zero at the other end,said third-harmonic Fourier coefficients being normalized by dividing bythe maximum value of said fundamental Fourier coefficient formaintaining the representation independent of the number of windings andthe impedance of the windings; said third-harmonic Fourier coefficientsbeing representative of a conductor distribution which is maximum atsaid one end of said quadrant at which said fundamental Fouriercoefficient is a maximum, and a minimum at said other end of saidquadrant, said distribution of horizontal deflection conductors of saidyoke being described in a quadrant by the sum of normalized fundamentaland third-harmonic horizontal Fourier coefficients, said normalizedfundamental horizontal Fourier coefficients increasing in value fromcross-sections taken near said entrance end to reach a maximum value atsaid exit end of said yoke, said normalized third-harmonic horizontalFourier coefficients having a negative value at cross-sections takennear the entrance end of said yoke and having a value which becomesincreasingly more positive at cross-sections taken towards themid-region of said yoke so as to take on a positive value near saidmid-region, and having a maximum positive value at cross-sections takennear said exit region whereby the distribution of conductors of saidhorizontal deflection winding is densely packed and subtends arelatively small portion of said quadrant at cross-sections taken nearsaid exit end, and is progressively less densely packed and subtends arelatively greater portion of each quadrant at cross-sections takenprogressively closer to said entrance end of said yoke; said verticaldeflection conductors being described in a quadrant by the sum ofnormalized fundamental and third-harmonic vertical Fourier coefficients,said vertical fundamental Fourier coefficients having a value atcross-sections taken near said entrance end of said yoke andprogressively decreasing in value at cross-sections taken progressivelycloser to said exit-end of said yoke, said normalized verticalthird-harmonic Fourier coefficients having values which are negative atcross-sections taken near said entrance end of said yoke and whichvalues become increasingly more positive at cross-sections taken atpositions progressively nearer the mid-region of said yoke, and havingmaximum positive values at cross-section taken near said exit-region ofsaid yoke, whereby said vertical winding exhibits a distribution in aquadrant which distribution has the greatest density near one end of thequadrant at cross-sections taken near said entrance end of said yokewhich greatest density progressively shifts toward the other end of saidquadrant at cross-sections taken progressively nearer said exit regionof said yoke; whereby the convergence of said color display apparatus isrendered substantially insensitive to the transverse position of saidyoke relative to said kinescope.